### 11.7 Synchrotron radiation from electrons

The magnetic field not only modifies the rates of neutrino emission processes, but also opens new
channels of neutrino emission. Let us consider a coordinate system such that . The electron
energy levels are then given by , where is the Landau quantum
number. The transverse component of the electron momentum is not conserved, and this allows for the
electron synchrotron radiation process,
where the notation is to remind us of the necessary presence of the magnetic field. For nonquantizing
() and nondegenerate nonrelativistic electrons, the neutrino emission rate is temperature
independent . But for a hot () ultra-relativistic () electron-positron
gas, we get a density independent (see [428]).